A software solution, unfortunately, is the easiest to circumvent.
The best solution, IMHO, would be a hardware solution, such as a SonicWall or other firewall that will do logging (either internally or through a syslog). I notice that some of the Linksys routers are now coming with Syslog capability.
You could drop something like that in, and set up the "other" computer with SysLog services, and every place either computer goes on the Internet will be logged. No software to install on the "monitored" machine, so there is nothing to circumvent.
Now, a few other things to consider:
1) Is there a company policy in place for acceptable use? If not, I would suggest you get one; unless the person is specifically looking at ILLEGAL (i.e. underage) porn, if you don't have a company policy to support action, you don't really have a leg to stand on.
2) As the person's manager, they need to ask themselves what they are hoping to accomplish. The goal of a good manager should be to have a better employee. If the goal is to get rid of the person....
3) And speaking of getting rid of the person... are you in a "right to work" state? If so, you don't even *need* a reason to let someone go. Unless they are union or in some other way protected.
The simplest solution (if the goal is to just correct the behavior and have a better employee) is to send out a memo to all employees reminding them of the acceptable use policy, and that since they are company computers they are subject to inspection at any time for acceptable use. I would make mention of "We reserve the right to monitor any network traffic on our corporate computers" etc. That is usually enough to scare someone into making sure they're staying appropriate.
<Laughs> In the past, when I've sent out something like this, I always get the "guilty conscience" people... "OMG... I was looking for ticket prices for my vacation next month... am I in trouble????" Stuff like that....
Just my 2¢
-Cole's Law: Shredded cabbage
--Greg